The value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].
What is Mean Value Theorem?Mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
Given.
Function is 2x+1 on the interval [3,6]
f(x)=2x+1
f(x) continuous on [3, 6] and differentiable on (3, 6) so the MVT applies here.
f(3)=7
f(6)=13
Average rate of change of f on [3,6]
= (13-7) / (6-3) = 6/3=2
To find the c-value guaranteed by the MVT, such that the instantaneous rate of change when x = c is 2, we differentiate, set f'(x) = 2, and solve:
f'(x) = 2 and x = 1.
c = 0 is the only c-value in the interval at which the instantaneous rate of change = the average rate of change.
Hence, the value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].
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Use two different methods to find and explain a formula for the area of a trapezoid
that has parallel sides of length a and b and height h. Consider these ideas or others: (a)
Combine two copies of the trapezoid to make a parallelogram. (b) Subdivide the trapezoid
into two triangles, one with base b and one with base a.
The two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}What is trapezoid?
A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
Area : ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sidesPerimeter : sum of lengths of sides of trapezoidNumber of vertices : 4Number of edges : 4Properties : Convex polygonType : QuadrilateralSum of interior angles : 360°We have a trapezoid.
Now, we can find the area in two ways -
[1] -
A = (1/2) × {a + b} × {h}
[2] -
A = {b x h} - (1/2) x {(b - a} x h}
Therefore, the two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}To solve more questions on trapezoids, visit the link below -
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Evaluate the expression when a=10 .
a/4+1/3 =
Answer:
Step-by-step explanation:
A cafeteria sold 36 cartons of regular flavored milk. If the ratio of regular milk sold to chocolate milk sold was 9:4, what is the combined amount of chocolate and regular milk sold?
Answer:
The combined amount of chocolate and regular milk sold was 52 cartons.
Step-by-step explanation:
1. Divide
36 ÷ 9 = 4
(This means that the ratio has a unit rate of 4. That means):
2. Second ratio rate
4 x 4 = 16
(Because the unit rate is 4).
3. Add
(Now, we add the original 36 cartons with the 16 cartons we found because the first step was just for finding the unit rate).
36 + 16 = 52 cartons.
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What occurs when you are dealing with objects that are round
static friction
sliding friction
rolling friction
Greg works two part time jobs. One job is at a gas station that pays $12 an hour and the other is delivering groceries for $15.50 an hour. Between the two jobs Greg wants to earn at least $390 a week. Let x be the number of hours he works at the gas station and let y be the number of hours he works delivering groceries. Write an inequality that models this situation.
The required inequality model for this situation is 12x + 15.5y ≥ 390.
What are inequalities?
The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. The equal sign is substituted between by the less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">,"< "," <="," or ">=."
For instance, x>3 (x should be greater than 3)
If there is just one variable, the inequality is said to have an open sentence.
Instance: x 6 (x is less than 6)
Double Inequalities: If the statement demonstrates a double relation between the expressions or the numbers, the inequality is said to be a double inequality.
Instance: 3 x 8 ( x is greater than or equal to 3 and less than 8)
Given, the gas station pays $12 an hour and delivers groceries for $15.50 an hour.
And, x be the number of hours he works at the gas station and let y be the number of hours he works delivering groceries.
Then, total earnings in gas station = 12x
total earnings for delivering groceries = 15.5y
So, based on the given inequality condition
12x + 15.5y ≥ 390
Hence, the required inequality model for this situation is 12x + 15.5y ≥ 390.
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As a project manager, you need to plan production runs over the next 3 1/2 weeks. If your team is able to produce 1,250 widgets in one week, how many widgets can they produce in 3 1/2 weeks?
Answer: 4,375.
Step-by-step explanation: If your team is able to produce 1,250 widgets in one week, then in 3 1/2 weeks, they will be able to produce 3 1/2 * 1,250 = <<3.5*1250=4375>>4,375 widgets.
if you have a square with a length of 5x, write an expression for the perimeter of the square.
The perimeter of a square with a length of 5x can be represented by the expression 45x. This is because the perimeter of a square is equal to the length of any side of the square multiplied by the total number of sides, which is 4 for a square. So, for a square with a length of 5x, the perimeter would be 45x, or 20x.
6. Alex says he can find the product for
(3 X 5) X 2 by solving 3 X (5 × 2).
Is Alex correct?
Answer: Yeah
Step-by-step explanation: Multiplication can be done in any order, so using parenthesis to denote which numbers to multiply first should not matter.
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Answer:
c) Propability of rolling doubles=6
Propability of rolling a sum grrater then or equal to 8 = 15
(Together add up to 21)
d)6 ->(1,1)(1,2)(1,3)(2,1)(2,2)(3,1)
e)9 ->(1,6)(3,4)(5,2)(3,5)(5,3)(3,6)(5,4)(5,5)(5,6)
The graph shows the amount of gas that Dario's car uses to travel different distances.
Complete the statement about the graph.
Gas Mileage
100
The number of miles is always
20
times
90
the number of gallons of gas.
80
70
Dario's car can travel
?
miles using
60
12 gallons of gas
Distance Traveled (miles)
50
40
30
20
.
10
0
0 1 2 3
4 5 6 7 8 9 10
Gas (gallons)
Answer: 46 miles
Step-by-step explanation: according to my calculations i minus te total mileage gas times the current philosphy of the number of gallons with 50 - 30
10/8 = n/10 proportions please
[tex]\displaystyle n=\frac{25}{2}[/tex]
Step-by-step explanation:A proportion is a set of equal ratios.
Cross Multiplication
The most common (and easiest) way to solve a proportion is cross multiplication. To cross-multiply, multiply the numerators by the opposite denominators. So, you are multiplying across the proportion.
After cross multiplying you get 10*10 = 8n.
Solving For n
Now, we can use algebra to find n.
100 = 8nJust, divide both sides by 8.
[tex]n=\frac{100}{8}[/tex]Then, simplify.
[tex]n=\frac{25}{2}[/tex]Checking The Answer
To check your answer all you have to do is plug n back into the equation.
[tex]\frac{10}{8}=\frac{25/2}{10}[/tex]This can be rewritten as
[tex]\frac{10}{8}= \frac{25}{2} *\frac{1}{10}[/tex]Then, the right side can be solved.
[tex]\frac{10}{8}= \frac{10}{8}[/tex]Please help me on this question and thank you!
Answer:
{YH, YT, BH, BT, TH, TT}
where Y = yellow, B = blue, T = turquoise
H = heads, T= tails
6 possible outcomes
Step-by-step explanation:
There are 2 independent events
Spinner which can land on one of three colors - Yellow(Y), Blue(B) and Turquoise(T)
Flipping a coin which has two outcomes Heads(H) and Tails(T)
Both events are independent of each other
So the sample space is:
{YH, YT, BH, BT, TH, TT}
Total of 6 outcomes
PLEASE ASAP I NEED HELP
Given the inequality 4x ≤ 28, which of the following is a solution that makes the inequality true?
The value of the inequality equation is x ≤ 7
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
4x ≤ 28 be equation (1)
Now , on simplifying the equation , we get
Divide by 4 on both sides of the inequality equation , we get
x ≤ 7
Therefore , the value of x is less than or equal to 7
All the numbers less than or equal to 7 satisfies the condition for x
The value of the equation x ≤ 7 is shown in the graph below
Hence , The value of the inequality equation is x ≤ 7
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write an algebraic expression that marshall can use to determine the total cost of buying a watermelon that weighs w pounds and some tomatoes that weigh t pounds. How much will it cost to buy a watermelon that weighs 18 1/2 pounds and 5 pounds of tomatoes if watermelon cost $0.68 and the tomatoes cost $3.25
Answer: The cost will be a total of $142.05. That is $125.80 for a Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.
Step-by-step explanation:
Given: Watermelons are 0.68 / lb and tomatoes are 3.25 / lb.
Let w = watermelon weight
Let t = tomato weight.
An equation would be:
.68w + 3.25t = Total cost
For 185 lb of Watermelon and 5 lbs of tomatoes:
.68(185) + 3.25(5) =
$125.80 + $16.25 = $142.05
Given the definitions of f(x) and g(x) below, find the value of (ƒ o g)(2).
f(x) = -x + 2
g(x) = x² – 5x – 2
Wdym by definition Answer:
Step-by-step explanation:
Given the ratio 8 ounces to 1 cup,how many ounces are in 4 cups?
Answer:
32 oz
Step-by-step explanation:
Given the ratio 8 ounces to 1 cup, how many ounces are in 4 cups?
4 * 8 oz = 32 oz
Find the area of a Shaded portion
Find the area of a Shaded portion.
D. 68
chris is 5 years older than 4 times arins age. the sum of their ages is less than 40. what is the oldest arin could be?
Answer: 6 years old.
Step-by-step explanation:
Chris: 5+4a
c + a<40
5 + 4a + a < 40
5a<35
a<7
For the oldest, let's assume Arin is 6, because it is the highest number that is less than 7.
Arin can be maximum of 6 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let the Arin's age be x.
So, Chris age is 4x + 5
Now, the sum of their ages is less than 40.
x+ 4x+ 5 < 40
5x < 35
x < 7
Hence, Arin can be maximum of 6 years old.
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What is the range of the function?
f(x)=3x−1−2
Enter your answer, in interval notation, in the box.
range:
The range of a function f(x)=3ˣ⁻¹-2 is (-2, ∞)
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known attempt to define function can be found in the writings of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability. The range of possibilities for variation or the distances between them: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.
Given,
f(x)=3ˣ⁻¹-2
Range=(-2, ∞)
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find the slope and y-intercept of the line 3x - 5y = 15
The slope of the given line, 3x - 5y = 15, is 3/5 and the y-intercept is -3
Determining the slope and y-intercept of a lineFrom the question, we are to determine the slope and y-intercept of the given line.
The given line is
3x - 5y = 15
To determine the slope, we will write the equation in the slope-intercept form of a line.
The slope-intercept form of a line is given as
y = mx + b
Where m is the slope
and b is the y-intercept
Now, we will express the given equation in this form
3x - 5y = 15
-5y = 15 - 3x
Divide through by - 5
y = -3 + 3/5x
y = 3/5x - 3
By comparing to the slope-intercept form of a line,
m = 3/5
and b = -3
Hence, the slope is 3/5 and the y-intercept is -3
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A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters. Is it a right triangle?
PLSSS HURRY !!!!!!!!!!
For the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters is the right triangle.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that, A triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters.
We have to verify whether it is a right-angle triangle or not.
A right-angle triangle must follow the Pythagoras theorem.
The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
If the longest side is the hypotenuse.
h²=p²+b²
LHS
68² = 1424
RHS
60²+25²
3600+625
4225
L.H.S=R.H.S
Thus, the triangle has sides with lengths of 25 centimeters, 60 centimeters, and 68 centimeters in the right triangle.
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Cari is searching online for airline tickets. Two weeks ago, the cost to fly from boston to denver was $220. Now the cost is $295. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percent increase with the additional baggage fee for airline would be $125 / $220 x 100% = 56.82%.
What is meant by the term percentage?A number can be expressed as a fraction of 100 using a percentage. It may be computed by dividing the number by the total and multiplying by 100. It is commonly represented by the sign "%". The percentage of men, for instance, would be 25/100 x 100, or 25%, if there were 100 persons in all.
In a variety of areas, including statistics, finance, and education, percentages are often employed. For instance, in finance, percentage increase in stock prices are used to gauge a market's or company's success. In education, grades are frequently given as percentages to represent class marks.
How to solve?
The increase in the cost of the ticket is $295 - $220 = $75
The percent increase is $75 / $220 x 100% = 34.09%.
If the airline charges an additional $50 baggage fee, the new ticket price would be $295 + $50 = $345.
The increase in the cost of the ticket with the additional baggage fee would be $345 - $220 = $125.
The percent increase with the additional baggage fee would be $125 / $220 x 100% = 56.82%.
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Suppose the following estimated regression equation was determined to predict salary based on years of experience.
Estimated Salary=22,717.59+2732.16(Years of Experience)
What is the estimated salary for an employee with 7 years of experience?
The estimated salary for an employee with 7 years of experience will be;
⇒ Estimated Salary = 41,842.71
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The estimated regression equation was determined to predict salary based on years of experience is,
⇒ Estimated Salary = 22,717.59 + 2732.16(Years of Experience)
Now,
Since, The equation is,
⇒ Estimated Salary = 22,717.59 + 2732.16(Years of Experience)
Hence, The estimated salary for an employee with 7 years of experience will be;
⇒ Estimated Salary = 22,717.59 + 2732.16 × 7
⇒ Estimated Salary = 22,717.59 + 19,125.12
⇒ Estimated Salary = 41,842.71
Thus, The estimated salary for an employee with 7 years of experience will be;
⇒ Estimated Salary = 41,842.71
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What is the average rate of change of this function on the interval from x = 1 to x = 3? f(x)=10(2)x Enter your answer in the box.
Answer:
30
Step-by-step explanation:
The way to figure out the average rate of change is to divide the change in f(x) and divide that by the change in x. A formula for this is [tex]\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}[/tex]
1.) By this definition, we need to figure out our x1 and x2. We can say the x1 = 3 and x2 = 1
2.) Next, we plug it into the formula. We will get [tex]\frac{f(3)-f(1)}{3-1}[/tex].
3.) If we simplify, we will get 10(2)^3 - 10*2 divided by 2, which is equal to 10*4 - 10 = 30.
-7(1+9a) have no idea how to do this
Answer:
-7-63a
Step-by-step explanation:
-7(1 + 9a)
(use the distributive property of multiplication to simplify)
-7-63a
need help with this one keep getting wrong answer
Answer:
try socratic
Step-by-step explanation:
Zeg has $9.20 left on a gift card to the candy store. He has the following items in his shopping basket: 2 giant lollipops, 3 popcorn balls, 1 candy bar and 5 candy sticks . Zeg wants to buy two more items name two more possible items he can buy using his gift card
Answer:
Zeg can buy a candy stick and a Popcorn ball.
Step-by-step explanation:
After calculating the total based on the following:
Candy bars are $0.99, Candy sticks are $0.45, Giant lollipops are $1.75, and Popcorn balls are $0.50.
the total was $8.24. [tex]9.20[/tex] [tex]-8.24 = 0.96[/tex] The only two items that can fit into this are a popcorn ball, and a candy stick.
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
the product of two numbers divided by 5
Step-by-step explanation:
xy/5
.........
....................
which property in math is (n+2.9)+0.3=n+(2.9+0.3)
Notice that the order the numbers are written on both sides is the same:
n, then 2.9, then 0.3
Because the order is the same and all that changed were the parentheses (the way the numbers were grouped), this is the associative property of addition.
The associative property is about the groupings. You can remember this by thinking about that fact that associations are groups.
2. How much is 50 percent of 1025